text:
Quantum Physics
The Wave Structure of Matter (WSM) and Spherical
Standing Wave Interactions explains Discrete Energy States of Quantum
Theory / Wave Mechanics). A Simple Solution to the Particle / Wave Duality
of Light and Matter, EPR, Non Locality & Quantum Entanglement.
Note: This article was written several years ago. It is long (by internet standards) and basically explains the main subjects of quantum theory from a Wave Structure of Matter foundation (wave mechanics). If you prefer shorter summaries just browse the quantum physics links on the right side of this page.
To begin, a few nice quotes on Quantum Physics.
On the one hand the quantum theory of light cannot be considered satisfactory since it defines the energy of a light particle (photon) by the equation E=hf containing the frequency f. Now a purely particle theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of light, to introduce the idea of a particle and that of frequency simultaneously. On the other hand, determination of the stable motion of electrons in the atom introduces integers, and up to this point the only phenomena involving integers in physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be considered simply as particles, but that frequency (wave properties) must be assigned to them also. (Louis de Broglie, Nobel Prize Speech, Quantum Physics, 1929)
The development during the present century is characterized by two theoretical systems essentially independent of each other: the theory of relativity and the quantum theory. The two systems do not directly contradict each other; but they seem little adapted to fusion into one unified theory. ... Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory do, really, correspond to the facts. ... de Broglie conceived an electron revolving about the atomic nucleus as being connected with a hypothetical wave train, and made intelligible to some extent the discrete character of Bohr's 'permitted' paths by the stationary (standing) character of the corresponding waves. (Albert Einstein, On Quantum Mechanics, 1940)
A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement. Quantum theory thus reveals a basic oneness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated 'basic building blocks', but rather appears as a complicated web of relations between the various parts of the whole. (Fritjof Capra, The Tao of Physics, On Quantum Theory)
Introduction to Quantum Physics
Quantum Theory / Wave Mechanics
From 1900 to 1930 there was a revolution in the foundations of our understanding of light and matter interactions. In 1900 Planck showed that light energy must be emitted and absorbed in discrete 'quanta' to explain blackbody radiation. Then in 1905 Einstein showed that the energy of light is determined by its frequency, where E=hf. Finally, in the late 1920s, de Broglie and Schrodinger introduced the concept of Standing Waves to explain these discrete frequency and energy states of light and matter (standing waves only exist at discrete frequencies and thus energy states).
So it is clear that Waves are central to Quantum Physics and our understanding of the structure and discrete energy states of Matter (which explains why Quantum Theory is also called Quantum Wave Mechanics). As we shall explain, the problems and absurdities of quantum theory have been caused by the continuing assumption of the discrete 'particle' concept for both light and matter, and thus the resulting paradox of the 'Particle / Wave' duality.
As we are dealing with a scientific theory, it is necessary to begin by stating the central Principles of the 'Metaphysics of Space and Motion and the Wave Structure of Matter', which describe how Matter exists in Space as a Spherical Standing Wave and interacts with other Matter in the Space around it. From this foundation we can then deduce the solutions to many problems currently found in Quantum Theory caused by this ancient concept that matter exists as 'particles'.
For example, the obvious solution to the paradox of the particle / wave duality of matter is to realise that the Wave-Center of the Spherical Standing Wave causes the observed 'particle' effects of Matter (see wave diagram below). Likewise, the discrete 'particle' properties of Light (quanta / photons) are caused by Standing Wave interactions which only occur at discrete frequencies and thus energy states.
I think it is useful to end this quantum physics introduction with two very important quotes. Firstly from Erwin Schrodinger;
What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). The world is given to me only once, not one existing and one perceived. Subject and object are only one. The barrier between them cannot be said to have broken down as a result of recent experience in the physical sciences, for this barrier does not exist. (Erwin Schrodinger, on Quantum Theory)
Because Schrodinger believed in real waves, he was never happy with Max Born's statistical / probability interpretation of the waves that became commonly accepted (and was actively promoted by Heisenberg and Bohr) in Quantum Theory / Mechanics.
Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics / quantum theory held today (1950s), I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. (Schrödinger E, The Interpretation of Quantum Mechanics. Ox Bow Press, Woodbridge, CN, 1995)
I don't like it, and I'm sorry I ever had anything to do with it. (Erwin Schrodinger talking about quantum theory.)
And I very strongly agree with Schrodinger (and greatly respect him) when he writes;
The scientist only imposes two things, namely truth and sincerity, imposes them upon himself and upon other scientists. (Schrodinger)
Secondly, David Bohm provides a clear account of how this incorrect 'particle' conception of matter not only causes harm to the Sciences, but also to the way we think and live, and thus to our very society and its future evolution.
The notion that all these fragments is separately existent
is evidently an illusion, and this illusion cannot do other than lead
to endless conflict and confusion. Indeed, the attempt to live according
to the notion that the fragments are really separate is, in essence, what
has led to the growing series of extremely urgent crises that is confronting
us today. Thus, as is now well known, this way of life has brought about
pollution, destruction of the balance of nature, over-population, world-wide
economic and political disorder and the creation of an overall environment
that is neither physically nor mentally healthy for most of the people
who live in it. Individually there has developed a widespread feeling
of helplessness and despair, in the face of what seems to be an overwhelming
mass of disparate social forces, going beyond the control and even the
comprehension of the human beings who are caught up in it.
(David Bohm, Wholeness and the Implicate Order, 1980)
Principle One - On What Exists and its Properties
i) One Thing, Space (Infinite and Eternal) Exists as a Wave-Medium and
contains Wave-Motions which Propagate at the Velocity of Light c.
ii) Matter Exists as the Spherical Wave Motion of Space (which determines)
the Size of our Finite Spherical Universe within an Infinite Space.
+ = This (very rough!) diagram shows how the Spherical In and Out Waves form a Standing Wave around the Wave-Center 'particle'.
Principle Two - On the Necessary Connections between What Exists
i) Any Change in Velocity of the Spherical In-Waves from One Direction
Changes where these In-Waves meet at their respective Wave-Center which
we see as the Accelerated Motion of the 'Particle'. (This is the Cause
of All Forces, i.e. Newton's Law of Inertia F=m.a, see Fig:2.1 below)
ii) The Spherical In-Waves are formed from the Huygens' Combination of
Out-Waves from All other Matter in our Finite Spherical Universe. (This
is the Cause of Mach's Principle - the Mass (mass-energy density of space) of an object
is determined by all the other matter in the Universe.)
So let us now explain and solve the many problems and paradoxes of Quantum Theory using the Two Principles of the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter.
During the years 1900-1930, many experiments were done on the interactions of light beams, particle beams, and metal targets. Analysis of these experiments showed that Light and Matter had both Particle and Wave properties. As we have said, the solution to this apparent paradox of the Particle/Wave duality is to simply explain how the discrete 'particle' properties (quanta) are in fact caused by standing Wave interactions.
To do this we must begin by explaining the experimental foundations
of Quantum Theory;
1. Max Planck's Discovery of the Particle (Quantum) Properties of Light,
E=hf. (1900)
2. de Broglie's Discovery of the Wave Properties of Electron Interactions,
y=h/mv. (1927)
3. The Equivalence of Energy, Mass and Frequency and the Compton Wavelength
Y of the Electron Y=h/mc = 2.43*10-12m.
1.1 Quantum Physics Foundations: Max Planck's Discovery of Particle / Quantum Properties of Light (1900)
In 1900 Max Planck made a profound discovery. He showed (from purely
formal / mathematical foundations) that light must be emitted and absorbed
in discrete amounts if it was to correctly describe observed phenomena
(i.e. Blackbody radiation).
Prior to then light had been considered as a continuous electromagnetic
wave, thus the discrete nature of light was completely unexpected, as
Albert Einstein explains;
About fifteen years ago (1899) nobody had yet doubted that a correct account of the electrical, optical, and thermal properties of matter was possible on the basis of Galileo-Newtonian mechanics applied to molecular motion and of Maxwell's theory of the electromagnetic field. (Albert Einstein, 1915)
Then Planck showed that in order to establish a law of heat radiation (Infra red light waves) consonant with experience, it was necessary to employ a method of calculation whose incompatibility with the principles of classical physics became clearer and clearer. For with this method of calculation, Planck introduced into physics the quantum hypothesis, which has since received brilliant confirmation. (Albert Einstein, 1914)
In the year nineteen hundred, in the course of purely theoretical (mathematical) investigation, Max Planck made a very remarkable discovery: the law of radiation of bodies as a function of temperature could not be derived solely from the Laws of Maxwellian electrodynamics. To arrive at results consistent with the relevant experiments, radiation of a given frequency f had to be treated as though it consisted of energy atoms (photons) of the individual energy hf, where h is Planck's universal constant. During the years following, it was shown that light was everywhere produced and absorbed in such energy quanta. In particular, Niels Bohr was able to largely understand the structure of the atom, on the assumption that the atoms can only have discrete energy values, and that the discontinuous transitions between them are connected with the emission or absorption of energy quantum. This threw some light on the fact that in their gaseous state elements and their compounds radiate and absorb only light of certain sharply defined frequencies. (Albert Einstein, 1940)
Even the Greeks had already conceived the atomistic nature of matter and the concept was raised to a high degree of probability by the scientists of the nineteenth century. But it was Planck's law of radiation that yielded the first exact determination - independent of other assumptions - of the absolute magnitudes of atoms. More than that, he showed convincingly that in addition to the atomistic structure of matter there is a kind of atomistic structure to energy, governed by the universal constant h, which was introduced by Planck. This discovery became the basis of all twentieth-century research in physics and has almost entirely conditioned its development ever since. Without this discovery it would not have been possible to establish a workable theory of molecules and atoms and the energy processes that govern their transformations. Moreover, it has shattered the whole framework of classical mechanics and electrodynamics and set science a fresh task: that of finding a new conceptual basis for all physics. Despite remarkable partial gains, the problem is still far from a satisfactory solution. (Albert Einstein, 1950)
Albert Einstein (1905) used Planck's relationship to explain the results
of the photoelectric effect which showed that the energy E
of ejected electrons was dependent upon the frequency f
of incident light as described in the equation E=hf.
It is ironic that in 1921 Albert Einstein was awarded the Nobel Prize
for this discovery, though he never believed in particles and acknowledged
that he did not know the cause of the discrete energy transfers (photons)
which were contradictory to his continuous field theory of matter!
In 1954 Albert Einstein wrote to his friend Michael Besso expressing his
All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)
Most importantly, Albert Einstein also suspected that Matter could not be described by a continuous spherical force field;
I consider it quite possible that physics cannot be based on the field concept, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics. (Albert Einstein, 1954)
Albert Einstein's suspicions were well justified, for he had spent a
lifetime trying (and failing) to create a unified field theory of matter
that explained both Quantum Theory / Light and Relativity / Gravity.
In fact Matter, as a Spherical Standing Wave which causes the 'Field'
effect, interacts with other matter in discrete standing wave patterns,
not with continuous force fields as he had imagined, thus his task was
ultimately impossible, as he sadly came to realise towards the end of
his life.
However, his work on the photoelectric effect confirmed that light energy was only emitted and absorbed by electrons in discrete amounts or quanta. This quanta of light energy soon became known as the 'photon' (i.e. discrete like a particle) and led to the paradox that light behaved both as a continuous e-m wave (Maxwell, Albert Einstein) as well as a discrete particle/photon (Planck, Albert Einstein). So we see that Albert Einstein was partly responsible for the discovery of the particle/photon concept of light, though he completely rejected the notion of discrete particles. He writes;
Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. (Albert Einstein)
Albert Einstein is correct that there are no discrete particles, and
that the particle can only appear as a limited region in space in which
the field strength or the energy density are particularly high. But it
is the high Wave-Amplitude of the Wave-Center of a Spherical Standing
Wave in Space (not of a continuous spherical force field) that causes
the particle effect. Thus of three concepts, particles,
force fields, and motion, it finally
turns out that Motion, as the spherical wave motion of space, is the correct
concept, as it then explains both particles and fields. (For further explanation
see Article on Relativity)
It is most important to realise though that Albert Einstein was correct
in imagining matter as being spatially extended, as he explains;
I wished to show that space time is not necessarily something to which one can ascribe to a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept empty space loses its meaning. (Albert Einstein)
It is certainly true that the particle and its forces / fields are very useful mathematical concepts, unfortunately, they also cause many problems and paradoxes because they are approximations to reality and do not physically exist.
We can now finally solve these problems by understanding the reason
for these discrete energy states, which are due to the fact that standing
waves only exist at discrete frequencies, like notes on the string of
a guitar, thus while the Spherical Standing Wave Structure of Matter predicts
that energy exchanges will be discrete, as observed, the continuous e-m
wave does not anticipate this.
Thus the Spherical Standing Wave Structure of Matter explains Max Planck's
(1900) discovery that there are only certain allowed discrete energy states
for electrons in molecules and atoms, and further, that light is only
ever emitted and absorbed by electrons in discrete or 'quantum' amounts,
as the electrons move from one stable standing wave pattern to another.
(This is explained in more detail in section 1.4)
1.2 Quantum Theory / Mechanics: de Broglie's Discovery of the Wave Properties of Electrons (1927)
The next step was taken by de Broglie. He asked himself how the discrete states could be understood by the aid of current concepts, and hit on a parallel with stationary (standing) waves, as for instance in the case of proper frequencies of organ pipes and strings in acoustics. (Albert Einstein, 1954)
It is with some frustration that I now read these quotes, as it is obvious in hindsight as to their errors, and how simply they can now be solved! de Broglie's realisation that standing waves exist at discrete frequencies and thus energies is obviously true and important, yet he continued with the error of the particle concept and thus imagined particles moving in a wavelike manner! Nonetheless, as he was close to the truth he had considerable success with his theory, and these predicted wave properties of matter were shortly thereafter confirmed from experiments (Davisson and Germer, 1927) on the scattering of electrons through crystals (which act as diffraction slits). As Albert Einstein confirms;
Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory does, really, correspond to the facts. (Albert Einstein, 1954)
So by 1927 the wave properties of matter had been predicted theoretically by de Broglie, and then confirmed by experiment. But unfortunately these scientists continued to believe in the existence of discrete particles, and thus they misinterpreted this most important discovery of the standing wave properties of matter.
1.2.1 de Broglie's Interpretation of the Standing Waves as the Wave-Like Motion of a Particle in Orbit (1927)
In 1913, Niels Bohr had developed a simple (though only partly correct) model for the hydrogen atom that assumed; (Our further comments in brackets)
i) That the electron particle moves in circular orbits about the proton
particle. (This is nearly correct, they are not 'orbits' but complex Standing
Wave patterns)
ii) Only certain orbits are stable. (This is nearly correct, only certain
Standing Wave patterns are resonantly stable)
iii) Light is emitted and absorbed by the atom when the electron 'jumps'
from one allowed orbital state to a another. (This is nearly correct,
the electrons move from one stable Standing Wave pattern to another. This
is known as 'Resonant Coupling' and is explained in Section 1.4.)
This early atomic model had some limited success because it was obviously
created to explain the discrete energy states of light emitted and absorbed
by bound electrons in atoms or molecules, as discovered by Planck in 1900.
de Broglie was aware of Bohr's model for the atom and he cleverly found
a way of explaining why only certain orbits were 'allowed' for the electron.
As Albert Einstein explains;
de Broglie conceived an electron revolving about the atomic nucleus as being connected with a hypothetical wave train, and made intelligible to some extent the discrete character of Bohr's 'permitted' paths by the stationary (standing) character of the corresponding waves. (Albert Einstein, 1940)
Fig: 1.2.1 The allowed discrete orbits of the electron as imagined
by de Broglie.
de Broglie assumed that because light had both particle and wave properties, that this may also be true for matter. Thus he was not actually looking for the wave structure of matter. Instead, as matter was already assumed to be a particle, he was looking for wave properties of matter to complement the known particle properties. As a consequence of this particle/wave duality, de Broglie imagined the standing waves to be related to discrete wavelengths and standing waves for certain orbits of the electron particle about the proton. (Rather than considering the actual standing wave structure of the electron itself.)
From de Broglie's perspective, and from modern physics at that time, this solution had a certain charm. It maintained the particle - wave duality for BOTH light and matter, and at the same time explained why only certain orbits of the electron (which relate to whole numbers of standing waves) were allowed, which fitted beautifully with Niels Bohr model of the atom. de Broglie further explains his reasoning for the particle/wave duality of matter in his 1929 Nobel Prize acceptance speech;
On the one hand the quantum theory of light cannot be
considered satisfactory since it defines the energy of a light particle
(photon) by the equation E=hf containing the frequency f. Now a purely
particle theory contains nothing that enables us to define a frequency;
for this reason alone, therefore, we are compelled, in the case of light,
to introduce the idea of a particle and that of frequency simultaneously.
On the other hand, determination of the stable motion of electrons in
the atom introduces integers, and up to this point the only phenomena
involving integers in physics were those of interference and of normal
modes of vibration. This fact suggested to me the idea that electrons
too could not be considered simply as particles, but that frequency (wave
properties) must be assigned to them also. (de Broglie,
The solution to their problems was first found by Wolff (1986). He discovered two things (both of which deserve a Nobel prize in their own right);
Firstly, from reading Feynman's PhD thesis (see reference, Feynman and
Wheeler, 1945) he was aware of Feynman's conception of charged particles
which 'somehow' generated Spherical Electromagnetic In and Out Waves (Feynman
called them advanced and retarded waves), but Wolff realised that there
are no solutions for spherical vector electromagnetic waves (which are
mathematical waves which require both a quantity of force and a direction
of force, i.e. vector). Wolff had the foresight to try using real waves,
which are Scalar (defined by their Wave-Amplitude only).
And this then led to a series of remarkable discoveries.
He realised that spherical In and Out-Waves removed the need for a separate
particle, as the Wave-Center of the Spherical Waves created the particle
He then discovered that when one spherical standing wave was moving relative
to another the Doppler shifts gave rise to BOTH the de Broglie
Wavelength AND the Mass increase of Albert Einstein's
Relativity. (i.e. Wolff demonstrated that when two charged particles
(Wave-Centers of two SSWs) are moving relative to one another they gives
rise to beats of interference (caused by the Doppler shifting of the In
and Out Waves due to relative Motion) which were identified in experiments
as the de Broglie wavelength y=h/mv, and also gave rise to the frequency
increases and thus energy/mass increases (as E=hf =mc2) of
Special Relativity.
Thus in the one equation he had deduced, with mathematical certainty,
the two observed phenomena due to relative motion, which respectively
found central parts of both Quantum Theory and Albert Einstein's Special
Relativity. (Thus for the first time uniting these two theories from one
common theoretical foundation!)
This then led to his further work on resonant coupling which finally solved
the puzzle of the 'photon' and explained why light energy is only ever
emitted and absorbed in discrete amounts. (See Section 1.4)
Unfortunately for modern physics, and ultimately for human knowledge, this obvious solution was never considered by de Broglie, Albert Einstein, Bohr, Schrodinger, Heisenberg, Dirac, Born, Feynman, etc. etc. Thus the now obvious solution of realising that matter was a Spherical Standing Wave that causes the point particle effect at the Wave-Center remained unknown and ignored, and instead, the confusing and paradoxical concept of the particle / wave duality was retained.
1.3 Quantum Theory: The Compton Wavelength 2.43*10-12m of the Electron Y=h/mc (1923)
As stated, in hindsight there were many clues as to the Wave Structure of the Electron. Another obvious clue being that the electron itself has a 'Compton' wavelength (named after American experimental physicist Holly Compton who discovered this from experiments with electron beams). But unfortunately they had come to accept the particle / wave duality of matter and simply continued to assume that somehow this paradoxical conception of matter was true, and thus beyond human comprehension. (So they stopped looking for an obvious solution!)
So let us briefly explain the Compton Wavelength. Experiments show that Energy is directly related to both Frequency and Mass (this is true since we now realise that they are ALL caused by Wave-Motion). As we know from experiment the energy E and mass m of the electron, and the velocity of light c, we can calculate the Compton Wavelength Y of the Electron as follows; E=hf=mc2 and f=c/Y, thus hc/Y= mc2 resulting in Y=h/mc which for the Electron = 2.43*10-12m.
Fig: 2.3 The Compton Wavelength (Y) of the Electron - While this wavelength is related to the actual Wavelength of the Spherical Standing Wave, it is more complex than this. As the Spherical In-Wave flows in towards the Wave-Center, both its Wave-Amplitude and mass-energy density of space increase, thus the velocity and wavelength will also change. (Thus there is still a substantial amount of mathematical analysis required on how the Wavelength of the Electron changes with distance from the Wave-Center.)
1.4 Quantum Wave Mechanics: The Schrodinger Wave Equations / Standing Wave Interactions (1928)
Quantum theory was thus essentially founded on the experimental observations of frequency and wavelength for both light and matter. These empirical facts are obviously consistent with the Spherical Standing Wave structure of matter.
1. Planck's discovery that energy is related to frequency in the equation
2. The Equivalence of Energy, Frequency and Mass E=hf=mc2,
which deduces the Compton Wavelength Y=h/mc
3. The de Broglie wavelength y=h/mv
It was Erwin Schrodinger who discovered that when frequency f and de Broglie wavelength y were substituted into general wave equations it becomes possible to express energy E and momentum mv (from the above equations) as wave functions - thus a confined particle (e.g. an electron in an atom/molecule) with known energy and momentum functions could be described with a certain wave function.
From this it was further found that only certain frequency wave functions, like frequencies on musical strings, were allowed to exist. These allowed functions and their frequencies depended on the confining structure (atom or molecule) that the electron was bound to (analogous to how strings are bound to a violin, and only then can they resonate at certain frequencies).
Significantly, these allowed frequencies corresponded to the observed discrete frequencies of light emitted and absorbed by electrons bound in atoms/molecules. This further confirmed the standing wave properties of matter, and thus that only certain standing wave frequencies could exist which corresponded to certain energy states. The agreement of observed frequencies and Schrodinger's Wave Equations further established the fundamental importance of Quantum Theory and thus the Wave properties of both light and matter. As Albert Einstein explains;
How can one assign a discrete succession of energy values E to a system specified in the sense of classical mechanics (the energy function is a given function of the co-ordinates x and the corresponding momenta mv)? Planck's constant h relates the frequency f =E/h to the energy values E. It is therefore sufficient to assign to the system a succession of discrete frequency f values. This reminds us of the fact that in acoustics a series of discrete frequency values is coordinated to a linear partial differential equation (for given boundary conditions) namely the sinusoidal periodic solutions. In corresponding manner, Schrodinger set himself the task of coordinating a partial differential equation for a scalar wave function to the given energy function E (x, mv), where the position x and time t are independent variables. (Albert Einstein, 1936)
And here we have a final piece of the puzzle in a sense, for it was Schrodinger who discovered that the standing waves are scalar waves rather than vector electromagnetic waves. This is a most important difference. Electromagnetic waves are vector waves - at each point in Space the wave equations yield a vector quantity which describes both a direction and an amplitude (size of force) of the wave, and this relates to the original construction of the e-m field by Faraday which described both a force and a direction of how this force acted on other matter.
Spherical Wave Motions of Space are Scalar waves - at each point in Space the wave equations yield a single quantity which simply describes the wave amplitude (there is no directional component). For example, sound waves are scalar waves where the wave amplitude describes the Motion (or compression) of the wave medium (air). Likewise Space is a nearly rigid Wave-Medium which propagates Wave-Motions.
With de Broglie's introduction of the concept of standing waves to explain the discrete energy states of atoms and molecules, and the introduction of scalar waves by Schrodinger, they had intuitively grasped important truths of nature as Albert Einstein confirms;
Experiments on interference made with particle rays have
given brilliant proof that the wave character of the phenomena of motion
as assumed by the theory does, really, correspond to the facts.
The de Broglie-Schrodinger method, which has in a certain sense the character
of a field theory, does indeed deduce the existence of only discrete states,
in surprising agreement with empirical facts. It does so on the basis
of differential equations applying a kind of resonance
argument. (Albert Einstein, 1927)
So let us now explain in more detail this phenomena of Light energy being emitted and absorbed in discrete amounts (photons) due to Resonant Standing Wave interactions. Firstly, we must understand Principle Two and realise that the velocity of wave Motions in Space is not constant, and in fact depends upon both the Wave-Amplitude and the mass-energy density of space (square of Wave-Amplitude). These are simply the properties of Space as a Wave-medium.
1.4.1 Quantum Physics: On the Forces of Charge and Light
It is the nature of Principles that they are stated rather than deduced. Thus we must state the Properties of Space, as Principles, and then demonstrate that logical deductions from these Principles do in fact correspond to observation. What we have found is that if Space behaves in the following way, then it gives rise to deductions which correspond to observation and experiment.
The Wave Velocity (velocity of light c) varies with both the Wave-Amplitude
and the mass-energy density of space (the square of the Wave-Amplitude).
i) The greater the Wave-Amplitude the greater the Wave-Velocity.
ii) The greater the mass-energy density of space the slower the Wave-Velocity.
We do not know why Space, as a Wave-Medium, behaves this way, other than
to say that these are simply the properties of Space. What we do discover
though, is that from these foundations we get a simple explanation of
both Charge/Light and Mass/Gravity.
As gravity is explained in the article on Relativity, the general idea is only briefly summarised here. When In-Waves travel in through other Matter / Wave-Motions of Space, they slightly slow down due to the increased mass-energy density of space, and this causes the Wave-Centers to naturally move together, which we observe as Gravitational attraction. As mass-energy density of space is always positive (squares are always positive), this always causes a slowing of the In-Waves, thus explaining why gravity is always attractive.
On the other hand, Wave-Amplitude is both positive and negative, thus
interacting Wave-Amplitudes can either increase or decrease (i.e. combine
or cancel out), causing either an increase or decrease in the velocity
of the In-Waves, and a consequent moving together, or moving apart of
the Wave-Centers.
It is this property of Space that causes Charge / Electromagnetic Fields
and in a slightly more complex manner, Light.
Thus when we place two electrons near one another in Space, then the Wave-Amplitude of Space between them increases because the Waves are in phase and the Wave-Amplitudes combine and increase, thus the Wave-Velocity increases (opposite to gravity's slowing of In-Waves) and this causes the Wave-Centers to move apart. This explains the electrical repulsion of like charges.
Conversely, if we place an electron and a positron (anti-matter being
the opposite phase Wave-Motion to Matter, thus a positron is the opposite
phase to an electron) then the Wave-Amplitude between the two Wave-Centers
tends to cancel out and become smaller, thus the Wave-Velocity between
the two Wave-Centers decreases (like gravity) and thus causes the Wave-Centers
to move together.
In fact this also explains the electron / positron (matter / antimatter)
annihilation, as the Wave-Centers will eventually overlap one-another
and the Wave-Amplitudes will completely cancel out (due to their equal
and opposite phase) and thus disappear.
This explains Charge, but does not explain Light, which is slightly more
complex, though it is still caused by the same fundamental properties
of Space.
1.4.2 Quantum Physics: On Resonant Coupling as the Cause of Light
What we must further realise is that Light is only emitted and absorbed by electrons bound in atoms or molecules, and these electrons have some complex repeating Standing Wave-Motion about the nucleus. Thus the electrons behave as 'oscillating resonators' and it is common knowledge to electrical engineers and physicists that two interconnected resonators can undergo resonant coupling, where one resonator decreases in frequency and the other one increases a corresponding amount.
Thus two bound resonating electrons (oscillators) exchange energy much like classical coupled oscillators, such as electric circuits or joined pendulums. The coupling provided by the non-linear centers of the resonances (high Wave-Amplitude Wave-Centers where the Wave-Velocities change ) causes them to change velocity, frequency, and wavelength, due to the interaction (modulation) of each other's waves. Since significant coupling can only occur between two oscillators which possess the same resonant elements, the frequency (energy) changes are equal and opposite. This we observe as the law of conservation of energy.
When opposite changes of frequency (energy ) takes place between two resonances, energy seems to be transported from the center of one resonance to another. We observe a loss of energy where frequency decreases and added energy where it increases. The exchange appears to travel with the speed of the IN waves of the receiving resonance which is c, the velocity of light. When large numbers of changes occur together, so we can sample part of it, we see a beam of light. When single exchanges occur we see photons as discrete energy exchanges. The transitory modulated waves traveling between two resonances (as the Electrons/Wave-Centers move from one standing wave pattern to another) create the illusion of the photon. An exchange may require 108 to 1015 cycles to complete, depending on the degree of coupling and species of resonance.
For example, if one oscillator were an electron, its frequency mc2/h is about 1023 hertz, and if the transition time were 10-8 seconds, the frequency change requires about 1015 cycles to complete. Such a large number of cycles implies, in engineering slang, a large Q value, which indicates great precision of the equal and opposite changes in oscillator frequency, and the conservation of energy
Fig: 1.4.2 Light is Caused by the Resonant Coupling of two bound Wave-Centers of Spherical Standing Waves (Electrons) with oscillating wave functions. This diagram is only an approximation, but it gives you some idea of the 'secondary' wavelength (the 'electromagnetic' wavelength of light) caused by the interactions of the In and Out-Waves of the two Electrons/Wave-Centers.
Thus we realise that these different standing Wave patterns cause a cyclical oscillation in the Shape of the In and Out-Waves which describes a wave function that is ultimately the cause of the 'electromagnetic' wavelength and frequency of light. As only certain discrete 'orbits' (standing wave functions) exist for the Wave-Center of the Spherical Standing Wave, then it can only exchange frequencies in discrete levels which correspond to discrete energy exchanges of light 'photons'. i.e. E=hf where only discrete frequencies (f) area resonantly stable and thus 'allowed'. (There are no separate light 'particles / photons' or collapsing wave functions, both being mathematical existents only!)
Most importantly, these standing wave interactions and resonant coupling are the reason for Schrodinger's Standing Wave Equations and their obvious success at explaining the allowed energy states for electrons in atoms, and thus the discrete photon effect of light as these electrons move from one resonant standing wave pattern (quantum state) to another.
1.5.1 Quantum Theory: Heisenberg's Uncertainty Principle
On Chance and Probability in a Necessarily Interconnected finite spherical Universe within a Non-Determined Infinite Space
At the same time that the wave properties of matter were discovered, two further discoveries were made that also profoundly influenced (and confused) the future evolution of modern physics.
Firstly, Werner Heisenberg developed the uncertainty principle which
tells us that we (the observer) can never exactly know both the position
and momentum of a particle. As every observation requires an energy exchange
(photon) to create the observed 'data', some energy (wave) state of the
observed object has to be altered. Thus the observation has a discrete
effect on what we measure. i.e. We change the experiment by observing
it! (A large part of their problem though was to continue to assume the
existence of discrete particles and thus to try to exactly locate both
their position and motion, which is impossible as there is no discrete
Further, because both the observed position and momentum of the particle
can never be exactly known, theorists were left trying to determine the
probability of where, for example, the 'particle' would be observed.
1.5.2 Quantum Mechanics: Born's 'Probability Waves' Interpretation of QT (1928)
Born (1928) was the first to discover (by chance and with no theoretical
foundation) that the square of the quantum wave equations (which is actually
the mass-energy density of space) could be used to predict the probability of where the
particle would be found. Since it was impossible for both the waves and
the particles to be real entities, it became customary to regard the waves
as unreal probability waves and to maintain the belief in the 'real' particle.
Unfortunately (profoundly) this maintained the belief in the particle/wave
duality, in a new form where the 'quantum' scalar standing waves had become
'probability waves' for the 'real' particle.
Albert Einstein unfortunately agreed with this probability wave interpretation,
as he believed in continuous force fields (not in waves or particles)
thus to him it was sensible that the waves were not real, and were mere
descriptions of probabilities. He writes;
On the basis of quantum theory there was obtained a surprisingly good representation of an immense variety of facts which otherwise appeared entirely incomprehensible. But on one point, curiously enough, there was failure: it proved impossible to associate with these Schrodinger waves definite motions of the mass points - and that, after all, had been the original purpose of the whole construction. The difficulty appeared insurmountable until it was overcome by Born in a way as simple as it was unexpected. The de Broglie-Schrodinger wave fields were not to be interpreted as a mathematical description of how an event actually takes place in time and space, though, of course, they have reference to such an event. Rather they are a mathematical description of what we can actually know about the system. They serve only to make statistical statements and predictions of the results of all measurements which we can carry out upon the system. (Albert Einstein, 1940)
It seems to be clear, therefore, that Born's statistical interpretation of quantum theory is the only possible one. The wave function does not in any way describe a state which could be that of a single system; it relates rather to many systems, to an 'ensemble of systems' in the sense of statistical mechanics. (Albert Einstein, 1936)
Albert Einstein is correct in one sense, mistaken in another. It is
true that matter is intimately interconnected to all the other matter
in the universe by the Spherical In and Out-Waves, something quantum theory
discovered but never correctly understood.
This has become known as quantum entanglement and relates to the famous
experiment posed by Albert Einstein, Podolsky, and Rosen (EPR) (see Section
1.7 for an explanation of this experiment) and when later technology allowed
its experimental testing, it confirmed quantum theory's entanglement.
Albert Einstein assumed this interconnectedness was due to the spherical
spatially extended field structure of matter, instead, it is due to the
interaction of the spherical spatially extended Standing Waves of matter
with other matter's Wave-Centers distant in Space. Explaining this Standing
Wave interaction of matter with other matter in the Space around it (action-at-a-distance)
is largely the purpose of this Article and is one of the great powers
of the Metaphysics of Space and Motion and the Spherical Wave Structure
of Matter.
Nonetheless, Albert Einstein was very close to the truth. He realised that because matter is spherically spatially extended we must give up the idea of complete localization and knowledge of the 'particle' in a theoretical model. For the particle is nothing but the Wave-Center of a Spherical Standing Wave, and thus can never be isolated as an entity in itself, but is dependent on its interactions with all the other Matter in the Universe. And it is this lack of knowledge of the system as a whole that is the ultimate cause of the uncertainty and resultant probability inherent in Quantum Theory.
Thus the last and most successful creation of theoretical
physics, namely quantum mechanics (QM), differs fundamentally from both
Newton's mechanics, and Maxwell's e-m field. For the quantities which
figure in QM's laws make no claim to describe physical reality itself,
but only probabilities of the occurrence of a physical reality that we
have in view. (Albert Einstein, 1931)
I cannot but confess that I attach only a transitory importance to this
interpretation. I still believe in the possibility of a model of reality
- that is to say, of a theory which represents things themselves and not
merely the probability of their occurrence. On the other hand, it seems
to me certain that we must give up the idea of complete localization of
the particle in a theoretical model. This seems to me the permanent upshot
of Heisenberg's principle of uncertainty. (Albert Einstein,
Albert Einstein believed that Reality could be represented by spherical force fields, that reality was not founded on chance (as Bohr and Heisenberg argued) but on necessary connections between things (thus his comment 'God does not play dice'!). He was largely correct, Matter is necessarily connected due to the Spherical Standing Wave Structure of Matter, but due to lack of knowledge of the system as a whole (the Universe), and the fact that it is impossible to determine an Infinite system (of which our finite spherical universe is a part - see Article on Cosmology), then this gives rise to the chance and uncertainty found in Quantum Theory.
1.6 Quantum Physics: A Brief Analysis of Feynman's Quantum Electrodynamics (QED, 1945)
QED is founded on the assumption that charged 'particles' somehow generate spherical electromagnetic (vector) In and Out Waves (a dynamic version of Lorentz's Theory of the Electron, as Feynman uses spherical electromagnetic Waves, rather than static force fields). It is important to realise though, that like most post-modern physicists, Richard Feynman was a Logical Positivist. Thus he did not believe in the existence of either particles or waves, he simply used this conceptual language as a way of representing how matter behaves in a logical way. As he says;
.. some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation. (Feynman)
This explains why he had such success and such failure at the same time, as he had the correct spherical wave structure of Matter, but he continued with two further errors, the existence of the particle, and the use of vector 'electromagnetic' waves (mathematical waves of force), rather than using the correct scalar 'quantum' waves. It is this error of Feynman's that ultimately led Wolff to make his remarkable discoveries of the WSM.
The problem for QED is twofold;
Firstly, there is the Problem of 'Renormalisation' - Feynman must assume finite dimensions for the particle, else the spherical electromagnetic waves would reach infinite fields strengths when the radius of the spherical electromagnetic waves tends to zero. There must be some non-zero cut-off that is arbitrarily introduced by having a 'particle' of a certain finite size. Effectively, Feynman gets infinities in his equations, and then he subtract infinity from infinity and puts in the correct empirical answer (which is not good mathematics, but it does then work extraordinarily well!)
Secondly, it is a mathematical fact that there are no vector wave solutions
of the Maxwell Equations (which found electromagnetic fields) in spherical
These are profound problems that have caused contradiction and paradox
within Quantum Theory to the present day, and have led to the self fulfilling
belief that we can never correctly describe and understand Reality.
... the more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that. (Feynman)
In fact Nature behaves in a very sensible and logical way (which explains why mathematical physics exists as a subject and can describe so many phenomena, and also explains how we 'humans' have been able to evolve a logical aspect to our minds!). That it is not Nature which is strange, but our incorrect conceptions of Nature! Most importantly, the simple sensible solutions to these problems can be easily understood once we know the correct Wave Structure of Matter.
1.6.1 The Solution to the Problem of 'Renormalisation'.
Richard Feynman's PhD thesis (with J. A. Wheeler, 1945) used Spherical
IN (Advanced) and OUT (Retarded) e-m waves to investigate this spherical
e-m field effect around the electron and how accelerated electrons could
emit light (e-m radiation) to be absorbed by other electrons at-a-distant
in space.
One vexing problem of this e-m field theory was that it led to infinitely
high fields (singularities) at the center of the point particle electron.
This was avoided with a mathematical process called renormalisation whereby
infinity was subtracted from infinity and the correct experimental result
was substituted into the equation. It was Dirac who pointed out that this
is not good mathematics - and Feynman was well aware of this!
In 1937 Paul Dirac wrote;
I must say that I am very dissatisfied with the situation, because this so called good theory does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small - not neglecting it just because it is infinitely great and you do not want it! (Dirac, 1937)
Richard Feynman was obviously also aware of this problem, and had this to say about renormalisation.
But no matter how clever the word, it is what I call a dippy process! Having to resort to such hocus pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self consistent. ... I suspect that renormalisation is not mathematically legitimate. (Feynman, 1985)
Albert Einstein was also aware of this problem as he explains in his critique of Lorentz's electromagnetic field theory for electrons (as it is still the same fundamental problem of the particle / electromagnetic field duality).
The inadequacy of this point of view manifested itself in the necessity of assuming finite dimensions for the particles in order to prevent the electromagnetic field existing at their surfaces from becoming infinitely large. (Albert Einstein, 1936)
Feynman's Spherical IN OUT wave theory is largely correct (and of course explains his success) but his error of using vector e-m waves resulted in infinities at the point particle as the radius tended to zero, and this led to the errors of renormalisation. In reality, Matter, as a structure of scalar spherical quantum waves, has a finite wave amplitude at the Wave-Center (as observed) and thus eliminates the infinities and the problems of renormalisation found in Feynman's Quantum Electrodynamics (QED).
1.6.2 The Solution to the Problem of there being NO Vector Wave Solutions of Maxwell's Equations in Spherical Co-ordinates
James Maxwell (1876) used the experimental (empirical) results of Faraday, Coulomb, etc. to develop four equations, now famous, whose solutions described an electromagnetic (e-m) wave which correctly deduced the velocity of light c. Maxwell was correct that light is a wave traveling with velocity c - but it is a wave developed from the interaction of the IN and OUT waves of two spherical standing waves whose Wave-Centers are bound in resonant standing wave patterns. (Thus it is the interaction of four waves which probably explains why there are four Maxwell Equations.)
The Maxwell's Equations (M.E.), which describe the formation of electric fields E by a charge distribution q and changing magnetic fields H, as well as the formation of the H field by a changing E and electric currents i, cannot describe a spherical electromagnetic wave! It is a mathematical fact that there are no wave solutions of the M.E.s in spherical co-ordinates! Only the scalar 'quantum' wave equation has spherical wave solutions. Similarly, there are no imaginable M.E. solutions for a 'photon particle'. It is clear that the M.E.s are not fundamental and the photon is only a mathematical construction.
The failure of the M.E. in spherical co-ordinates can be imagined by saying, You cannot comb the hair on a tennis ball. This means that if you attempt to comb down an E field (the hair representing the electric vector) everywhere flat onto a tennis ball (a spherical surface), you must create a 'cowlick' somewhere on the ball which frustrates your attempt to comb it.
The questions arise, Why did theorists continue to favour the e-m field,
the photon, and M.E. for 70 years in spite of the well-known flagrant
failure of the mathematical description to agree with observation? Why
were alternative descriptions of nature not sought? We suspect the answer
is because it worked once the errors were removed with a bit of 'hocus
pocus' mathematics and the aid of empirical data.
Unfortunately, this logical positivist view to retain the point particle
and vector force fields has been the root cause of the many paradoxes
and mysteries surrounding quantum theory. The resulting confusion has
been increasingly exploited in the popular press. Instead of searching
for the simple behaviour of nature, the physics community found that 'wave-particle
duality' was an exciting launching pad for more complex proposals that
found support from government funding agencies. The search for truth was
put into limbo and wave-particle duality reigned.
Once we understand though, that the particle theory of matter is a mathematical (logical positivist) description of nature, then it becomes less confusing. Essentially the particle is a mathematical construction to describe energy exchange. It says nothing about the energy exchange mechanism and thus makes no comment about how the particle exists, how it moves through Space, what the Space around the particle is made of, and how matter particles 'emit' and 'absorb' photon particles with other matter particles distant in Space.
Let us then consider one fundamentally important argument of Feynman's that light must be a particle.
For many years after Newton, partial reflection by two
surfaces was happily explained by a theory of waves,* but when experiments
were made with very weak light hitting photomultipliers, the wave theory
collapsed: as the light got dimmer and dimmer, the photomultipliers kept
making full sized clicks - there were just fewer of them. Light
behaves as particles.
* This idea made use of the fact that waves can combine or cancel out,
and the calculations based on this model matched the results of Newton's
experiments, as well as those done for hundreds of years afterwards. But
when experiments were developed that were sensitive enough to detect a
single photon, the wave theory predicted that the clicks of a photomultiplier
would get softer and softer, whereas they stayed at full strength - they
just occurred less and less often. No reasonable model could explain this
This state of confusion was called the wave - particle duality of light.
(Feynman, 1985)
Feynman though is incorrect in two ways;
Firstly, he is making unjustified assumptions beyond what is observed.
It is true that light energy is emitted and absorbed in discrete amounts
between two electrons. But we DO NOT OBSERVE any 'Particles' - we only
observe discrete energy exchanges!
Secondly, the solution is to realize that the Spherical Standing Wave
Structure of Matter actually demands that all energy exchanges for light
be of discrete amounts because this is what occurs for 'Resonant Coupling',
and for standing Wave interactions in general.
It is also interesting to see how simply Feynman summarizes QED;
So now, I present to you the three basic actions, from
which all the phenomena of light and electrons arise.
-Action #1: A photon goes from place to place.
-Action #2: An electron goes from place to place.
-Action #3: An electron emits or absorbs a photon.
This can now be simplified to two actions with the WSM;
Action #1: An Electron, as the Wave-Center of a Spherical Standing Wave,
goes from place to place in Space (as determined by the spherical In-Waves.)
Action #2: An Electron resonantly couples with another Electron (emits
or absorbs a photon)
Once we realise that there are no separate electron or photon particles, thus we remove the problem as to how an electron particle can interact with a separate photon particle! Thus this solution is actually more consistent (and simpler) than Feynman's QED, particularly when we consider Feynman's further explanation of a positron being an electron which goes backwards in Time.
The backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except that it is attracted to normal electrons - we say it has a positive charge. For this reason it's called a positron. The positron is a sister particle to the electron, and is an example of an anti-particle. ..This phenomena is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle. (Feynman, 1985)
As Wolff explains this is simply a mathematical truth caused by the
fact that a negative time in the wave equations changes the phase of the
standing waves to be equal and opposite, which corresponds to antimatter.
(Antimatter does no move 'backwards in time'!)
Further, notice what Feynman says about photons, which are treated as
particles in QED, and thus by Feynman's logic there should also be anti-photons,
whereas the WSM is clear on this point - there are anti-electrons (positrons)
which are opposite phase Spherical Standing Waves, but there are no separate
photon particles, thus no anti-photons!
And what about photons? Photons look exactly the same in all respects when they travel backwards in time, so they are their own anti-particles. You see how clever we are at making an exception part of the rule! (Feynman, 1985)
While it may be clever, it is not good philosophy, and it has led to
a very confused and absurd modern physics. Surely it is time for physicists
to start considering the fundamental theoretical problems of the existing
theories and to appreciate that the Metaphysics of Space and Motion and
the Spherical Wave Structure of Matter is a simple, sensible, and obvious
way to solve these problems!
Finally, let us explain how we can experimentally confirm the Spherical
Wave Structure of Matter (which would obviously be very convincing to
the skeptics!)
1.7 Quantum Theory: Wolff's Explanation of the Einstein, Podolsky, Rosen (EPR) Experiment & Further Predictions
'The Ultimate Paradox - Bell's Theorem' by Milo Wolff, Exploring the Physics of the Unknown Universe, 1994
In l935, Albert Einstein, Podolsky, and Rosen (EPR) put forward a gedanken
(thought) experiment whose outcome they thought was certain to show that
there existed natural phenomena that quantum theory could not account
for. The experiment was based on the concept that two events cannot influence
each other if the distance between them is greater than the distance light
could travel in the time available. In other words, only local events
inside the light sphere can influence one another.
Their experimental concept was later used by John Bell (1964) to frame
a theorem which showed that either the statistical predictions of quantum
theory or the Principle of Local Events is incorrect. It did not say which
one was false but only that both cannot be true, although it was clear
that Albert Einstein expected The Principle to be affirmed.
When later experiments (Clauser & Freedman 1972; Aspect, Dalibard,
and Roger, 1982; and others) confirmed that quantum theory was correct,
the conclusion was startling. The Principle of Local Events failed, forcing
us to recognize that the world is not the way it appears. What then is
the real nature of our world?
The important impact of Bell's Theorem and the experiments is that they
clearly thrust, a formerly only philosophical dilemma of quantum theory,
into the real world. They show that post-modern physics' ideas about the
world are somehow profoundly deficient. No one understood these results
and only scant scientific attention has been paid to them.
Figure 1.7.1 Experiment to test Bell's theorem Polarized photons are emitted at the center, pass through the adjustable polarization filters on the left and right, and enter detectors on each side. Coincidences (simultaneous detection) are recorded and plotted as a function of the angular difference between the two settings of the polarization filters.
The Essence of Bell's Theorem
His theorem relates to the results of an experiment like the one shown in Figure 1.7.1 (see above): A source of two paired photons, obtained from the simultaneous decay of two excited atomic states, is at the center. At opposite sides, are located two detectors of polarized photons. The polarization filters of each detector can be set parallel to each other, or at some other angle, freely chosen. It is known that polarizations of paired photons are always parallel to each other, but random with respect to their surroundings. So, if the detector filters are set parallel, both photons will be detected simultaneously. If the filters are at right angles, the two photons will never be detected together. The detection pattern for settings at intermediate angles is the subject of the theorem.
Bell (and Albert Einstein, Podolsky, and Rosen) assumed that the photons
arriving at each detector could have no knowledge of the setting of the
other detector. This is because they assumed that such information would
have to travel faster than the speed of light - prohibited by Albert Einstein's
Special Relativity. Their assumption reflects the Principle of Local Causes,
that is, only events local to each detector can affect its behaviour.
Based on this assumption, Bell deduced that the relationship between the
angular difference between detector settings and the detected coincidences
of photon pairs was linear, like line L in Figure 1.7.2. His deduction
comes from the symmetry and independence of the two detectors, as follows:
A setting difference of X, at one detector has the same effect as a difference
X, at the other detector. Hence if both are moved X, the total angular
difference is 2X and the total effect is twice as much, which is a linear
Figure 1.7.2 The result of an experiment to test Bell's theorem Data points R of the experiments are shown with black dots. They agree with the line QM, predicted by the quantum mechanics, and do not agree with the line L, predicted by Albert Einstein's concept of causality.
This was a big surprise, because the failure of causality suggests that
the communication is taking place at speeds greater than the velocity
of light.
The curved line is the calculation obtained from standard quantum theory.
Bell, Albert Einstein, Podolsky, and Rosen, or anyone who does not believe
in superluminal speeds, would expect to find line L.
In fact, the experiments yielded points R, which agreed with line QM.
The predictions of quantum theory had destroyed the assumptions of Albert
Einstein, Podolsky and Rosen!
The results of these experiments were so disbelieved that they were repeated
by other persons, using different photon sources, as well as particles
with paired spins. The most recent experiment by Aspect, Dalibard, and
Roger, used acousto-optical switches at a frequency of 50MHz which shifted
the settings of the polarizers during the flight of the photons, to completely
eliminate any possibility of local effects of one detector on the other.
Nevertheless, they reported that the EPR assumption was violated by five
standard deviations, whereas quantum theory was verified within experimental
error (about 2%).
Do Non-local Influences Exist?
Bell's Theorem and the experimental results imply that parts of the universe
are connected in an intimate way (i.e. not obvious to us) and these connections
are fundamental (quantum theory is fundamental). How can we understand
them? The problem has been analysed in depth (Wheeler & Zurek 1983,
d'Espagnat 1983, Herbert 1985, Stapp 1982, Bohm & Hiley 1984, Pagels
1982, and others) without resolution. Those authors tend to agree on the
following description of the non-local connections:
1. They link events at separate locations without known fields or matter.
2. They do not diminish with distance; a million miles is the same as
an inch.
3. They appear to act with speed greater than light.
Clearly, within the framework of science, this is a perplexing phenomenon.
In some mysterious quantum way, communication does appear to take place
faster than light between the two detectors of the apparatus. These results
showed that our understanding of the physical world is profoundly deficient.
Explaining the EPR-Bell 'Instant' Communication
The Spherical Wave Structure of Matter, particularly the behaviour of
the In and Out Waves, is able to resolve this puzzle so that the appearance
of instant communication is understood and yet neither Albert Einstein
nor QM need be wrong. In order to show this, it is necessary to carefully
look at the detailed process of exchanging energy between two atoms, by
the action of the IN/OUT waves of both atoms. Remember that for resonant
coupling it is necessary for the In and Out Waves of both electrons to
interact with one another. The passage of both In-Waves through both Wave-Centers
precedes the actual frequency shifts of the source and detector. A means
to detect this first passage event is not a capability of the usual photo-detector
apparatus and remains totally unnoticed. But the In-Waves are symmetrical
counterparts of the Out-Waves and carry the information of their polarization
state between parts of the experimental apparatus before the Out-Waves
cause a departing photon event. The IN-waves travel with the speed of
light so there is no violation of relativity.
At this point you may be inclined to disbelieve the reality of the In-Wave.
But there is other evidence for it. Remember, it explains the de Broglie
wavelength and thereby QM. It is necessary to explain the relativistic
mass increase of a moving object or the symmetry in its direction of motion.
It is responsible for the finite force of the SR electron at its center.
Are all of these merely coincidence? Especially, it is the combination
of In and Out Waves which explains these laws, not just the In-Waves.
If you believe in one you are forced to believe in the other.
(Note added by Haselhurst - In fact without In-Waves there can be no Out-Waves,
as the Out-Waves are simply the In-Waves after they have propagated In
and Out through the Wave-Center. Thus effectively Wolff is saying that
the electrons in the experiment are already interconnected with one another,
and hence are already 'aware' of one another's resonant state and polarization,
before the paired photons are emitted. It is this subtle interconnection
of Matter that explains the apparent conflict of the EPR experiment.)
Can Proof of the In-Waves be Found?
For someone to really believe a new theory, an experiment to
show the existence of new phenomena not previously known is most persuasive.
To prove the existence of the In-Waves (and thus the pre-existing interconnection
of the electrons with the rest of the apparatus) would be just such a
critical experiment. This can likely be accomplished with an apparatus
of the type used by Aspect, Dalibard, and Rogers (1982) except that instead
of making a random filter setting during a photon's passage time, the
filter setting should occur during the time period preceding photon departure.
The purpose is to frustrate communication by the In-Waves. As the In-Waves
are necessary to the energy exchange process, then the result of the experiment
would be a linear relation between the angular difference of the two filters.
This would be the result originally expected by Albert Einstein for the
EPR experiment.
(End of Section from Milo Wolff.)
The Wave Structure of Matter is a profound new way of looking at how Matter exists and interacts with other matter in Space. Wolff has explained a very simple change to a very famous experiment that currently causes Quantum Theory, and Human intellectual knowledge in general, profound problems and paradoxes. Thus it seems to us absolutely essential that this experiment be re-done as suggested above. We sincerely hope that this work on the Metaphysics of Space and Motion and the Spherical Wave Structure of Matter will ultimately lead to this new 'Paradigm' being taken seriously, and that this experiment will be performed sooner rather than later!
Quantum Theory (1900-1930) discovered four main things;
a) Both matter and light sometimes behave as particles and sometimes behave
as waves. (Planck, de Broglie)
b) Schrodinger's Standing Wave equations can be used to describe the allowed
discrete energy states for electrons (Wave-Centers) in atoms or molecules.
c) It is impossible to know both the location and momentum of a particle
and this inherent uncertainty can be calculated using the square of the
Wave equation to determine the probability of where the particle will
be found. (Heisenberg, Born)
d) Matter seems to be subtly interconnected with other matter in the Universe.
(EPR Experiment)
With the Metaphysics of Space and Motion and the Wave Structure of Matter
we can now sensibly explain these phenomena;
a) The solution of the particle/wave duality of matter is obvious - Matter
is a Spherical Standing Wave which creates a 'particle effect' at the
Wave-Center'. The solution to the particle/wave duality of light is more
complex (though it is still obvious once known) and is a consequence of
the standing wave structure of matter and that only discrete standing
wave interactions can occur during 'Resonant Coupling' of two bound electrons.
b) Schrodinger's Wave equations confirm this discrete standing wave interaction,
that only certain discrete standing wave frequencies between matter are
resonantly stable which causes frequency (and thus energy) exchanges to
be in discrete 'quanta' which can be mathematically explained as 'particle/photon'
c) Because Spherical Standing Waves are the size of the Universe, their
In-Waves are interacting with all the other matter in the Universe. As
we exist as complex arrangements of Wave-Centers here on earth, we do
not have immediate knowledge of how these In-Waves are interacting with
this other matter in the universe, and must simply wait until the In-Waves
arrive at the Wave-Center where we observe these changes in motion and
position of the Wave-Center. This lack of knowledge causes the uncertainty
as to how a Wave-Center will move about over time and thus qualitatively
explains why probability based upon wave equations can describe this uncertainty.
d) The Albert Einstein, Podolsky, Rosen (EPR) experiment performed by
Aspect in 1972 famously and controversially confirmed the apparent instant
interconnection of particles and contradicted Albert Einstein's Relativity
which requires that all matter to matter interactions be limited by the
velocity of light. Albert Einstein is in fact correct, the error of the
experiment was to assume matter was a particle rather than the Wave-Center
of a Spherical Standing Wave. Once this is understood then it explains
how matter is subtly interconnected with other matter in the Space around
it (by the In and Out-Waves) and leads to a minor change in the experiment
which will confirm the Metaphysics of Space and Motion and the Spherical
Wave Structure of Matter as a sensible and obvious solution to the problems
and paradoxes of not only Quantum Theory, but also of Albert Einstein's
Relativity and Cosmology.
Einstein, Albert Ideas and Opinions, Crown Trade
Paperbacks, 1954
Einstein, Albert Relativity, Crown Trade Paperbacks, 1961
Feynman, Richard and Wheeler, John Interactions with the Absorber
as the Mechanism of Radiation PhD Thesis- Palmer Physical Laboratory,
Princeton University, Princeton, New Jersey, 1945
Feynman, Richard P. The Strange Theory of Light and Matter, Penguin,
Help Humanity
"You must be the change you wish to see in the world."
(Mohandas Gandhi)
"When forced to summarize the general theory of relativity in one sentence:
Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. ... The particle can only appear as a limited region in space in which
the field strength or the energy density are particularly high. ...
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Expectations and asset prices: Keynes meets Hayek
Is the ECB right to buy up sovereign bonds in southern Europe? This column argues that the answer depends on who is right: Keynes or Hayek.
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Is the ECB right to buy up sovereign bonds in southern Europe? This column argues that the answer depends on who is right: Keynes or Hayek.
The financial crisis has vividly put into question the alignment of asset prices and fundamental values. For an example of this, look no further than at the current decision made by the ECB president, Mario Draghi, to launch a courageous programme (dubbed Outright Monetary Transactions) to prop up the prices of short-term bonds issued by EU member states that ask for the help of the European stability funds (EFSF and ESM). The thrust of the argument is fairly simple: in the current market conditions, peripheral EU states find it hard to fund themselves in the market, and are forced to pay dearly to convince investors to buy their bonds. This impairs the monetary policy transmission mechanism, which relies on the interest rate set by the ECB. Thus, allowing the ECB to act as a 'buyer of last resort' in the secondary market ensures that bond prices don't spike, hopefully taming interest rates and contributing to restoring the workings of EU monetary policy.
Two important and related ideas underlie this argument. The first is that bond prices in some EU states do not accurately reflect underlying fundamental values. The second one is that that such fundamentals are better impounded in some form of consensus view about those countries' ability to service their debt. In other words, there appears to be a disconnect between the asset price that market actors contribute to generate with their trades, and the view that several market participants have about the 'true' underlying value that such prices should reflect. Such a situation is far from a novel one.
Indeed, a basic model of asset prices which follows a somewhat simplistic version of the Efficient Market Hypothesis posits that trading among rational investors leads prices to gravitate around the consensus estimate (or average expectations) of underlying value given available information (see for example Marks 2011). Keynes thought that this vision does not correspond with the functioning of markets. Indeed, in the General Theory, he distinguished between "enterprise," or the activity of forecasting the prospective yield of assets over their whole life (where the investor focuses on the "long-term prospects and those only"), and short-term speculation. Keynes thought that while enterprise could anchor prices to fundamentals, in modern stock markets "speculation" would be king. This view contrasts with the ideas of Hayek on the informational efficiency of the market and the modern tradition of rational expectations analysis where market prices are aggregators of the dispersed information in the economy.
There have been quite a few attempts in the literature to explain financial pricing anomalies with recourse to behavioural theories and persistent differences in information. Without denying the plausibility of those approaches, in a recent paper (Cespa and Vives 2012), we address the tension between the Keynesian and the Hayekian visions in a dynamic market where investors have no behavioural bias and hold a common prior belief on the liquidation value of the risky asset. We show that the failure of the simplistic Efficient Market Hypothesis and reported anomalies in asset pricing can be explained in a standard rational expectations model as long as we generalise the model to encompass residual uncertainty on the liquidation value of the asset (so that the collective information of investors is not sufficient to recover the liquidation value) and allow liquidity trading to follow a general process. In other words, rejecting the simplistic Efficient Market Hypothesis does not necessarily imply subscribing to a behavioural view of the stock market.
We find that, in most cases, the simplistic version of the Efficient Market Hypothesis does not hold because long-term investors find it profitable to engage in short-term speculation due to the predictability of the aggregate demand. Low liquidity trades' persistence together with opaque fundamentals make the evolution of the aggregate demand, and thus of the asset returns, predictable. This lures investors towards the exploitation of these regularities, partially diverting them from the activity of evaluating the fundamentals. As a result, the equilibrium price ends up reflecting both components of investors' strategies (long and short term speculation), decoupling its dynamic from that of the consensus opinion.
In a stationary environment, investors speculate on the difference between the price and the fundamental value of the asset and prices are aligned with their average expectations about this value. In this context, the price is just a noisy measure of investors' consensus opinion, and the simplistic Efficient Market Hypothesis holds. In a dynamic market, investors speculate also on short-run price differences. With heterogeneous information, this may misalign prices and investors' average expectations, potentially leading prices either closer or farther away from the fundamentals compared to consensus. Two key deep parameters, the level of residual payoff uncertainty (that is, the residual uncertainty left after all the information on the asset value is pooled) and the degree of persistence of liquidity trades (that is, the extent to which the positions of liquidity traders revert over time), determine whether prices predict fundamentals better than consensus. When there is no residual uncertainty on the asset liquidation value and liquidity trading follows a random walk then prices are aligned with consensus like in a stationary market. This is one of the boundary cases where rational investors do not have incentives to speculate on short-run price movements. For a given, positive level of residual uncertainty, low persistence deteriorates the predictive power of prices in relation to consensus; conversely, high liquidity trades' persistence has the opposite effect. This yields a Keynesian region, where prices are farther away from fundamentals than average expectations, and a Hayekian region where the opposite occurs. The boundary of these regions reflects Keynes' situation where investors concentrate on the long-term prospects and where the simplistic version of the Efficient Market Hypothesis holds. In the Keynesian region short run price speculation based on market making motives (reversion of liquidity trades) predominates, while in the Hayekian region short run price speculation based on information (trend chasing) predominates (see Figure 1).
Figure 1
Notes: The figure shows the Hayekian and Keynesian regions drawn for different values of traders' risk aversion in the (ß, 1/τδ) space, where 0 < ß < 1 and 1/τδ > 0 , capture, respectively, the persistence of liquidity trades (with ß = 0 not persistent, and ß = 1 a random walk), and the degree of residual uncertainty on the liquidation value of the asset. The Keyesian (Hayekian) region lays to the left (right) of each curve.
Thus our theory explains when traders accommodate the aggregate demand, and when instead they chase the trend, relating these strategies to the informational properties of asset prices compared to consensus.
The Keynesian and Hayekian regions can be characterised in terms of investors' consensus opinion about the systematic behavior of future price changes. Indeed, in the Hayekian region, investors chase the market because the consensus opinion is that prices will systematically continue a given trend in the upcoming trading period. In the Keynesian region, instead, investors accommodate the aggregate demand because the consensus opinion is that prices will systematically revert. The Keynesian and Hayekian regions, however, do not coincide with the regions where momentum (that is, price run-ups) and reversal (that is, returns to trend) may occur. The reason is that the consensus opinion depends on the signal extraction problem investors face in the presence of heterogeneous information while momentum and reversal are evaluated ex ante from the perspective of an uninformed investor. In fact, reversal and momentum can happen at the frontier between the Keynesian and Hayekian regions, and therefore the simplistic version of the Efficient Market Hypothesis does not preclude return predictability (see Figure 2).
Figure 2
Notes: The Figure shows the interaction between the Hayekian and Keynesian regions (respectively denoted by the letters H and K) and the regions in which momentum or reversal occur (respectively denoted by the letters M and R) in (ß, 1/τδ) space.
In summary, the Efficient Market Hypothesis, in its simplistic version, does not hold in a standard but general dynamic asset pricing model with rational agents, and prices may depart substantially from consensus opinions. To return to the price of sovereign bonds: if we are in the Keynesian region, Mr. Draghi may be right to intervene since prices are far away from fundamentals compared to consensus estimates. However, if we are in the Hayekian region the consensus estimates are farther away from fundamentals than prices, and intervention is not warranted on the grounds of prices being out of line with fundamentals.
ReferencesBarberis, N and R Thaler (2003), "A survey of behavioral finance", in GM Constantinides, M Harris, and R Stulz (eds.), Handbook of the Economics of Finance.
Cespa, G and X Vives (2012), "Dynamic Trading and Asset Prices: Keynes vs. Hayek", Review of Economic Studies, 79(2):539-580.
Marks, H (2011), The Most Important Thing: Uncommon Sense for the Thoughtful Investor, Columbia University Press.
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But you have, Socrates, said Glaucon: and you, Thrasymachus, need be under no anxiety about money, for we will all make a contribution for Socrates.
Yes, he replied, and then Socrates will do as he always does-- refuse to answer himself, but take and pull to pieces the answer of some one else.
Why, my good friend, I said, how can any one answer who knows, and says that he knows, just nothing; and who, even if he has some faint notions of his own, is told by a man of authority not to utter them? The natural thing is, that the speaker should be some one like yourself who professes to know and can tell what he knows. Will you then kindly answer, for the edification of the company and of myself ?
Glaucon and the rest of the company joined in my request and Thrasymachus, as any one might see, was in reality eager to speak; for he thought that he had an excellent answer, and would distinguish himself. But at first he to insist on my answering; at length he consented to begin. Behold, he said, the wisdom of Socrates; he refuses to teach himself, and goes about learning of others, to whom he never even says thank you.
That I learn of others, I replied, is quite true; but that I am ungrateful I wholly deny. Money I have none, and therefore I pay in praise, which is all I have: and how ready I am to praise any one who appears to me to speak well you will very soon find out when you answer; for I expect that you will answer well.
Listen, then, he said; I proclaim that justice is nothing else than the interest of the stronger. And now why do you not me? But of course you won't.
Let me first understand you, I replied. justice, as you say, is the interest of the stronger. What, Thrasymachus, is the meaning of this? You cannot mean to say that because Polydamas, the pancratiast, is stronger than we are, and finds the eating of beef conducive to his bodily strength, that to eat beef is therefore equally for our good who are weaker than he is, and right and just for us?
That's abominable of you, Socrates; you take the words in the sense which is most damaging to the argument.
Not at all, my good sir, I said; I am trying to understand them; and I wish that you would be a little clearer.
Well, he said, have you never heard that forms of government differ; there are tyrannies, and there are democracies, and there are aristocracies?
Yes, I know.
And the government is the ruling power in each state?
And the different forms of government make laws democratical, aristocratical, tyrannical, with a view to their several interests; and these laws, which are made by them for their own interests, are the justice which they deliver to their subjects, and him who transgresses them they punish as a breaker of the law, and unjust. And that is what I mean when I say that in all states there is the same principle of justice, which is the interest of the government; and as the government must be supposed to have power, the only reasonable conclusion is, that everywhere there is one principle of justice, which is the interest of the stronger.
Now I understand you, I said; and whether you are right or not I will try to discover. But let me remark, that in defining justice you have yourself used the word `interest' which you forbade me to use. It is true, however, that in your definition the words `of the stronger' are added.
A small addition, you must allow, he said.
Great or small, never mind about that: we must first enquire whether what you are saying is the truth. Now we are both agreed that justice is interest of some sort, but you go on to say `of the stronger'; about this addition I am not so sure, and must therefore consider further.
I will; and first tell me, Do you admit that it is just or subjects to obey their rulers?
I do.
But are the rulers of states absolutely infallible, or are they sometimes liable to err?
To be sure, he replied, they are liable to err.
Then in making their laws they may sometimes make them rightly, and sometimes not?
When they make them rightly, they make them agreeably to their interest; when they are mistaken, contrary to their interest; you admit that?
And the laws which they make must be obeyed by their subjects,-- and that is what you call justice?
Then justice, according to your argument, is not only obedience to the interest of the stronger but the reverse?
What is that you are saying? he asked.
I am only repeating what you are saying, I believe. But let us consider: Have we not admitted that the rulers may be mistaken about their own interest in what they command, and also that to obey them is justice? Has not that been admitted?
Then you must also have acknowledged justice not to be for the interest of the stronger, when the rulers unintentionally command things to be done which are to their own injury. For if, as you say, justice is the obedience which the subject renders to their commands, in that case, O wisest of men, is there any escape from the conclusion that the weaker are commanded to do, not what is for the interest, but what is for the injury of the stronger?
Nothing can be clearer, Socrates, said Polemarchus.


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Coleman attorney: Appeal won't come this week
One day after the three-judge panel issued its final ruling in the U.S. Senate recount trial, Republican Norm Coleman's attorney reiterated plans to appeal the case to the Minnesota Supreme Court.
After a seven-week trial, the judges ruled that DFLer Al Franken received 312 more votes than Coleman in the election, and should get an election certificate. The court rejected all of Coleman's arguments to the contrary.
Attorney Ben Ginsberg said Coleman still believes that thousands of absentee ballots that should have been counted were not, because counties used different standards.
The panel ruled that Coleman failed to prove that mistakes or irregularities in the treatment of absentee ballots would have altered the outcome of the election.
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During a late morning conference call with reporters, Ginsberg said the Coleman campaign will file its appeal within the required 10 days, but probably not before next week.
"We're reviewing a 65-page opinion, and I think we'll take time to be sure we review it and frame the issues correctly before we file the notice," said Ginsberg.
Ginsberg claims the judicial panel failed to address problems with Minnesota's election system and instead defended it, thereby disenfranchising voters.
"We're reviewing a 65-page opinion, and I think we'll take time to be sure we review it and frame the issues correctly before we file the notice."
In its unanimous ruling, the judges noted that no election is perfect, but they said the overwhelming evidence is that the election was conducted fairly, impartially and accurately.
The timing for the appeal is important because Minnesota is short a senator while the case moves through the courts. Once a notice of appeal is filed, the sides will have more time to submit written arguments.
It's possible for Coleman to initiate a new action in federal court, too.
Coleman's lawyers have said their appeal will mostly center on violations of the constitutional guarantee of equal protection.
They say some counties treated absentee ballots differently, some rigorously checking to make sure voters met all legal requirements and others allowing more flexibility in applying the state standard.
Ginsberg said the trial court made things worse by requiring the campaigns to prove voters strictly abided by the law before the panel would count a previously rejected absentee ballot.
Franken's attorneys argued that no election is absolutely precise and that all counties operated under the same standard.
A key question for the high court is what tolerance for error is acceptable. The three-judge panel said local officials used "reasonable discretion to address election issues unique to their jurisdictions while still operating under the uniform standards of Minnesota law."
Either side can appeal an eventual state Supreme Court decision to the U.S. Supreme Court or throw the disputed election before the U.S. Senate, which can judge the qualifications of its members.
(The Associated Press contributed to this report)


text: In the middle text of the Rosetta Stone we find the names and functions of many gods. As a result of their titles, which literally meant a characteristic of the language and writing of the ancient Macedonians, we were able to identify names of several Egyptian gods even in the original way that they were called in ancient Egyptian. In the analyzed text we also found the names, most probably, of all the gods of the ancient Macedonians.


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National Institutes of Health
Progress Against Cancer May Be Greater Than Thought
Gains in saving patients' lives are obscured by increase in lifespans, study says
Monday, January 20, 2014MONDAY, Jan. 20, 2014 (HealthDay News) -- Although the death toll from cancer hasn't shrunk by as much in recent decades as that of diseases such as heart disease, significant progress has been made, a new study finds.
The problem in tabulating the full extent of recent gains against cancer is that efforts to beat back other diseases have also been successful, the researchers said.
"As fewer and fewer people die from heart disease, stroke and accidents, more and more people are alive long enough to be at risk of developing and dying from cancer," study principal investigator Samir Soneji, an assistant professor at the Geisel School of Medicine at Dartmouth College, said in a statement provided by Dartmouth-Hitchcock Medical Center.
For example, the study found that deaths from heart disease declined by 62 percent between 1970 and 2008. During the same period, deaths from accidents fell by more than a third.
Deaths from cancer, however, dipped by only 12 percent, the researchers said.
As part of their research, Soneji's team accounted for progress against cancer in the context of people avoiding other illnesses or accidents and living longer. Cancer risk increases with advancing age, making it more likely that today's longer-lived Americans will someday develop the disease, the researchers said.
"We estimate how the years of life lost from cancer are directly affected by cancer mortality and indirectly affected by increased cancer incidence because of greater longevity due to improvements in primary prevention, detection and treatment of other diseases," Soneji said.
In this context, the researchers found signs of significant progress in cutting cancer death rates.
For example, lung cancer deaths dropped dramatically between 1985 and 2005, mainly due to people quitting smoking, Soneji said. But the decline in these deaths wasn't as great as it could have been because more people were avoiding death from other causes -- and living long enough to develop lung cancer.
Overall progress in limiting deaths from colon, prostate and breast cancers has also been seen, the researchers said.
"Our approach reveals more accurately the aggregate contribution of cancer prevention, screening and treatment on progress against cancer," Soneji said.
The study was published Jan. 13 in the Journal of Clinical Oncology.
SOURCE: Dartmouth-Hitchcock Medical Center, news release, Jan. 14, 2014
Copyright (c) 2014 HealthDay. All rights reserved.
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